Don L. answered • 03/03/17

Tutor

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Fifteen years teaching and tutoring basic math skills and algebra

Hi Chanvadee, for part a), you are given the mid-point of the line BC, which is (3, 0). Using the equation to determine the mid-point of a line,

mid-point = ((x

_{1}+x_{2})/2, (y_{1}+y_{2})/2), you can solve for point B.Let (x

_{1}, x_{2}) be represented by point C, or (2, -1), and (x_{2}, y_{2}) represent point B.mid-point = (3, 0) = ((2+x

_{2})/2, (-1+y_{2})/2)Gives:

(2+x

_{2})/2 = 3, and (-1+y_{2})/2 = 0Solving for x

_{2}:(2+x

_{2})/2 = 32 + x

_{2}= 6x

_{2}= 4Solving for y

_{2}:(-1+y

_{2})/2 = 0-1 + y

_{2}= 0y

_{2}= 1Point B is at: (4, 1)

Part b)

The equation for the line DC will have the same slope as the line x + 4y = 8 and will have an x-intercept of (4, 0).

The slope of line x + 4y = 8 is represented by: -A/B, where A is the coefficient of the x-term and B is the coefficient of the y-term. -A/B equals: -1/4.

The line, in y-intercept form is: y = (-1/4) * x + 0, or y = -1/4 * x

For the equation of the line AD, first find the slope using the points for A and D, (-1, 4), and (4, 0).

The slope of AD = (4 - 0)/(-1 - 4), or -4/5

Using the slope-intercept form of the line and the point, (4, 0), we can find the line for AD.

y - y

_{1}= m * (x - x_{1})y - 0 = -4/5 * (x - 4)

Multiply by 5 to clear the fraction:

5y = -4 * (x - 4)

5y = -4x + 16

In standard form, the line is: 4x + 5y = 16

Questions?